Theorems · Theorem · measure theory
essSup_uniformOn_eq_ciSup
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} [inst : ConditionallyCompleteLattice β] {f : α → β} [Nonempty α]
[MeasurableSingletonClass α] [Finite α],
BddAbove (Set.range f) → essSup f (ProbabilityTheory.uniformOn Set.univ) = ⨆ a, f a- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- Set.rangestatement and proof · cited by 4,705
- Set.univstatement · cited by 3,945
- mul_oneproof · cited by 3,885
- Finitestatement and proof · cited by 3,029
- iSupstatement · cited by 2,415
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- MeasurableSingletonClassstatement and proof · cited by 230
- ENat.toENNRealproof · cited by 103
- ENat.cardproof · cited by 89
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